Sharp Growth Rate for Generalized

When a hypersurface (t) evolves with normal velocity equal to its mean curvature plus a forcing term g(x; t); the generalized (viscosity) solution may be \fattened" at some moment when (t) is singular. This phenomenon corresponds to nonuniqueness of codimension-one solutions. A speciic type of geometric singularity occurs if (t) includes two smooth pieces, at the moment t = 0 when the two pieces touch each other. If each piece is strictly convex at that moment and at that point, then we show that fattening occurs at the rate t 1=3 : That is, for small positive time, the generalized solution contains a ball of IR n of radius ct 1=3 , but its complement meets a ball of a larger radius 0 t 1=3 : In this sense, the sharp rate of fattening of the generalized solution is characterized. We assume that the smooth evolution of the two pieces of (t); considered separately, do not cross each other for small positive time.